Jan Denef: Diophantine sets over Z[T ] Proceedings of the A.M.S. 69.1, 1978  Home/Search   Document Not in Database   Summary   Related Articles

....presentation of Z[T ] The recursive presentations were introduced by Michael Rabin in a general setting, see [Rabin] He called them structures of recursive ring. Our principal ingredient will be the following theorem of Jan Denef. For the proof, see in appendix or in the original paper [Denef 3] Theorem 6.2 Let LT be the appropriate language for the polynomial ring Z[T ] For all recursive presentations of Z[T ] the corresponding relation R (n; F ) n 2 N F = n) is LT diophantine in Z[T ] We will call any relation R over Z[T ] recursively enumerable over Z[T ] iff its ....

....and the fact that N is a diophantine algebraic structure, we have shown that ae(u; v) is a diophantine relation in N . We have chosen the notations such that some similarities with Theorem 5.3 would be emphasized. 22 Let us speak now about the Theorem of Denef. We present the original proof from [Denef 3] 66 CHAPTER 8. APPENDIX We remember first to have denoted by Ym (T ) the second component of a solution (X; Y ) for the Pell equation P T : X 2 Gamma (T 2 Gamma 1)Y 2 = 1 over any polynomial ring, and the fact that the relation m 2 N F = Ym is diophantine over Z[T ] is equivalent ....

Jan Denef: Diophantine sets over Z[T ] Proceedings of the A.M.S. 69.1, 1978

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC